Geography Reference
In-Depth Information
Taylor expansion:
l
=
=
L
+
l
t
x
t
x
+
l
t
y
t
y
+
l
t
z
t
z
+
l
α
α
+
l
β
β
+
l
γ
γ
+
l
s
s
+
l
A
δA
+
l
E
δE
2
,
(21.20)
b
=
=
B
+
b
t
x
t
x
+
b
t
y
t
y
+
b
t
z
t
z
+
b
α
α
+
b
β
β
+
b
γ
γ
+
b
s
s
+
b
A
δA
+
b
E
δE
2
,
subject to
∂l
∂t
x
(
t
x
=
t
y
=
t
z
=0
,α
=
β
=
γ
=0
,s
=0
,A
1
=
a
1
,E
2
=
e
2
)
l
t
x
:=
(21.21)
etc. and
a
1
,δE
2
:=
E
2
e
2
, δE
=(2
E
)
−
1
δE
2
.
δA
:=
A
1
−
−
(21.22)
Box 21.4 (Curvilinear conformal coordinate transformation (datum transformation) extended
by ellipsoid parameters close to identity, Jacobi matrix).
⎡
⎤
t
x
t
y
t
z
α
β
γ
s
δA
δE
2
⎣
⎦
y
=
l
=A
−
L
+O
2
lb
=A
x
+O
2
x
.
(21.23)
b
−
B
Jacobi matrix:
A:=
∂
(
l,b
)
∂
(
t
x
,t
y
,t
z
,α,β,γ,s,A
1
,E
2
)
2
×
9
,
taylor
∈
R
(21.24)
t
x
=
t
y
=
t
z
=
α
=
β
=
γ
=
s
=0
,Λ
1
=
a
1
,E
2
=
e
2
taylor :=
{
}
.
Chain Jacobi matrix:
A:=J
23
J
1
=
∂
(
l,b
)
∂
(
x, y, z
)
∂
(
x, y, z
)
∂
(
t
x
,t
y
,t
z
,α,β,γs,A
1
,E
2
)
,
(21.25)
taylor
taylor
∂
(
x, y, z
)
∂
(
l,b,h
)
−
1
=
∂
(
l,b,h
)
∂
(
x, y, z
)
,
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